V-Pyramid Geometric Model
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This example demonstrates the geometric construction and dynamic changes of a V-pyramid with adjustable number of sides. Core mathematical concepts include solid geometry, limits, sequences, quadratic functions, volume calculation, and expected value. The construction highlights the use of GeoGebra commands like Pyramid, Rotate, and objects such as n2, A, B, C, D, E, a, faceABCD, faceADE, faceCDE, faceBCE, faceABE, edgeAD, edgeCD, edgeBC, edgeAB, edgeAE, edgeDE, edgeCE, edgeBE, H_2, n1, E_1, F_1, B_1, C_1, G_1, E_2, D_2, C_2, G_2, دکمه1, α, G, H, F, b, face4, face1, face3. Suitable for high school and above students studying solid geometry, calculus, and mathematical modeling.
GeoGebra Commands & Parameters
Pyramid(A, D, C, B, E) → a, faceABCD, edgeAE, edgeDE, edgeCE, edgeBE, faceADE, faceCDE, faceBCE, faceABE, edgeAD, edgeCD, edgeBC, edgeABRotate(G_2, α, edgeCD) → GRotate(E_2, α, edgeCD) → HRotate(H_2, α, edgeCD) → FPyramid(D_2, C_2, G, F, H) → b, face4, edge3, edge5, edgeGH, edgeFH, face1, face3, faceFGH, face2, edge1, edge4, edgeFG, edge2Rotate(F_1, α, edgeBC) → IRotate(E_1, α, edgeBC) → JRotate(G_1, α, edgeBC) → KPyramid(B_1, I, K, C_1, J) → c, face8, edge8, edgeIJ, edgeJK, edge9, face6, faceIJK, face7, face5, edge7, edgeIK, edge10, edge6
AI Drawing Prompt Reference
Draw a V-pyramid with an adjustable number of sides, showing its geometric construction and dynamic changes. The base is a quadrilateral with the apex directly above the center. Rotate the base edges and vertices to construct the pyramid's faces, forming multiple triangular surfaces. The final shape includes interconnected triangular and quadrilateral faces, demonstrating volume calculation and mathematical modeling concepts.
The prompt above was compiled from the original drawing commands and is for reference only.